Method and system for packing products with increased efficiency across packaging levels

ABSTRACT

This disclosure relates generally to automated packing of objects, and, more particularly, to a method and system for packing products with increased efficiency across packaging levels. While conventional methods of improving packaging efficiency focus on only one of the multiple levels in the packaging process, most commonly the tertiary level, the present disclosure attempts increasing packaging efficiency across packaging levels. Embodiments of present disclosure achieves increased efficiency across packaging levels by identifying standard size of secondary packages for packing a plurality of primary packages, packing the secondary packages within tertiary packages using a Mixed Integer Linear Programming (MILP) optimization model based on packing heuristics, and providing a feedback between tertiary and secondary packaging levels to identify standard secondary packages which can pack the primary packages with higher packing efficiency.

PRIORITY CLAIM

This U.S. patent application claims priority under 35 U.S.C. § 119 to:India Application No. 202021023183, filed on Jun. 2, 2020. The entirecontents of the aforementioned application are incorporated herein byreference.

TECHNICAL FIELD

The disclosure herein generally relates to automated packing of objects,and, more particularly, to a method and system for packing products withincreased efficiency across packaging levels.

BACKGROUND

Any product must be packed before it is transported to distributioncenters or consumers. Packaging usually involves three stages: primary,secondary, and tertiary. Primary packaging refers to packaging done atthe manufacturing site and contains the product, for example, a bottleis a primary package for wine which is a product. Secondary packaginginvolves packing primary packages into cartons (most often, cuboidal) sothat they can be loaded into containers or trucks for transportation.Similarly, tertiary packaging refers to packing the secondary cartons incontainers or pallets or trucks so that they are shipped to distributioncenters or customers. Most of the distribution companies are looking atautomated online bin packing wherein the parcels keep arriving on aconveyor and a robot or a robotic arm picks them up and places them inopen bins/packages efficiently.

Fill-rate is a metric used for defining efficiency of packing at thesecondary and tertiary levels. Fill-rate is calculated as ratio of totalvolume of the product(s)/carton(s) being placed to the volume of thecarton/container they are being placed into. Essentially this capturesthe space or volume utilization of the carton or container which isbeing packed.

According to a study done by DHL, the average fill-rate efficiency atthe secondary level is around 76%. In some cases, this may even dropdown to 60%. On the other hand, the average packing efficiency of astate-of-the-art online bin-packing algorithm (for example,Reinforcement Learning, first-fit, column-building, floor-building) forpacking at tertiary level hovers in the range of 50-67%. The overallpacking efficiency from primary level to tertiary level is therefore,around 30% on the lower end, and it increases up to 51% on the higherend.

Most of the existing automated packaging processes used in literaturethat aim at improving packaging efficiency attempt to focus on only oneof the multiple levels in the packaging process, most commonly thetertiary level. However, efficiency of packaging at one level is boundto affect the other levels. Thus, achieving maximum possible efficiencyconsidering the entire end to end packaging process is desired.

SUMMARY

Embodiments of the present disclosure present technological improvementsas solutions to one or more of the above-mentioned technical problemsrecognized by the inventors in conventional systems. For example, in oneembodiment, a method for packing products with increased efficiencyacross packaging levels is provided.

The method comprises obtaining a dataset comprising primary dimensionsof a plurality of primary packages, wherein the primary dimensionsinclude length, breadth, and height of each of the plurality of primarypackages. Further the method comprises applying a clustering techniqueon the primary dimensions of the plurality of primary packages to createa plurality of clusters of the plurality of primary packages, whereineach of the plurality of clusters has a subset of packages from theplurality of primary packages. The method further comprises identifyingsecondary dimensions for a plurality of standard secondary packages,wherein each of the plurality of standard secondary packages isassociated with a corresponding cluster among the plurality of clustersand has the secondary dimensions equal to maximum of each of the primarydimensions of the subset of packages within the corresponding cluster.Each of the subset of primary packages within each of the plurality ofclusters is packed inside a secondary package having secondarydimensions equal to the standard secondary package of correspondingcluster to obtain a plurality of secondary packages, each having aprimary package packed within it. Further the method comprisescalculating secondary packing efficiency for each of the plurality ofsecondary packages, wherein the secondary packing efficiency iscalculated as ratio of total volume of the primary packages within thesecondary package to the volume of corresponding secondary package.Furthermore, the method comprises packing each of the plurality ofsecondary packages within one or more tertiary packages based on MixedInteger Linear Programming (MILP) optimization model comprising anobjective function which maximizes space utilization within the one ormore tertiary packages, based on a plurality of heuristics, subject to aplurality of constraints including geometric constraints, orientationconstraints, stability constraints and tight packing constraints. Themethod further comprises calculating tertiary packing efficiency foreach of the one or more tertiary packages, wherein the tertiary packingefficiency is calculated as ratio of total volume of secondary packageswithin the tertiary package to volume of corresponding tertiary package.The method further comprises multiplying average of the secondarypacking efficiency of each of the subset of primary packages and averageof the tertiary packing efficiency of each of the one or more tertiarypackages to get a product of packing efficiencies; and selectingstandard secondary packages and corresponding clusters whose product ofpacking efficiencies is maximum, wherein the selected standard secondarypackages are utilized for packing newly obtained primary packages toachieve increased efficiency across packaging levels.

In another aspect, a system for packing products with increasedefficiency across packaging levels is provided. The system comprises amemory storing instructions; one or more Input/Output (I/O) interfaces;and one or more hardware processors coupled to the memory via the one ormore I/O interfaces, wherein the one or more hardware processors areconfigured by the instructions to obtain a dataset comprising primarydimensions of a plurality of primary packages, wherein the primarydimensions include length, breadth, and height of each of the pluralityof primary packages. Further the one or more hardware processors areconfigured to apply a clustering technique on the primary dimensions ofthe plurality of primary packages to create a plurality of clusters ofthe plurality of primary packages, wherein each of the plurality ofclusters has a subset of packages from the plurality of primarypackages. Further the one or more hardware processors are configured toidentify secondary dimensions for a plurality of standard secondarypackages, wherein each of the plurality of standard secondary packagesis associated with a corresponding cluster among the plurality ofclusters and has the secondary dimensions equal to maximum of each ofthe primary dimensions of the subset of packages within thecorresponding cluster. Each of the subset of primary packages withineach of the plurality of clusters is packed inside a secondary packagehaving secondary dimensions equal to the standard secondary package ofcorresponding cluster to obtain a plurality of secondary packages, eachhaving a primary package packed within it. Further the one or morehardware processors are configured to calculate secondary packingefficiency for each of the plurality of secondary packages, wherein thesecondary packing efficiency is calculated as ratio of total volume ofthe primary package within the secondary package to the volume ofcorresponding secondary package. Furthermore, the one or more hardwareprocessors are configured to pack the secondary packages within one ormore tertiary packages based on Mixed Integer Linear Programming (MILP)optimization model and one or more heuristics, wherein the MILPoptimization model comprising an objective function which maximizesspace utilization within the one or more tertiary packages, based on aplurality of heuristics, subject to a plurality of constraints includinggeometric constraints, orientation constraints, stability constraintsand tight packing constraints. Further the one or more hardwareprocessors are configured to calculate tertiary packing efficiency foreach of the one or more tertiary packages, wherein the tertiary packingefficiency is calculated as ratio of total volume of secondary packageswithin the tertiary package to volume of corresponding tertiary package.The one or more hardware processors are further configured to multiplyaverage of the secondary packing efficiency of each of the subset ofprimary packages and average of the tertiary packing efficiency of eachof the one or more tertiary packages to get a product of packingefficiencies; and select standard secondary packages and correspondingclusters whose product of packing efficiencies is maximum, wherein theselected standard secondary packages are utilized for packing newlyobtained primary packages to achieve increased efficiency acrosspackaging levels.

In yet another aspect, there are provided one or more non-transitorymachine readable information storage mediums comprising one or moreinstructions, which when executed by one or more hardware processorscauses a method for packing products with increased efficiency acrosspackaging levels. obtaining a dataset comprising primary dimensions of aplurality of primary packages, wherein the primary dimensions includelength, breadth, and height of each of the plurality of primarypackages. Further the method comprises applying a clustering techniqueon the primary dimensions of the plurality of primary packages to createa plurality of clusters of the plurality of primary packages, whereineach of the plurality of clusters has a subset of packages from theplurality of primary packages. The method further comprises identifyingsecondary dimensions for a plurality of standard secondary packages,wherein each of the plurality of standard secondary packages isassociated with a corresponding cluster among the plurality of clustersand has the secondary dimensions equal to maximum of each of the primarydimensions of the subset of packages within the corresponding cluster.Each of the subset of primary packages within each of the plurality ofclusters is packed inside a secondary package having secondarydimensions equal to the standard secondary package of correspondingcluster to obtain a plurality of secondary packages, each having aprimary package packed within it. Further the method comprisescalculating secondary packing efficiency for each of the plurality ofsecondary packages, wherein the secondary packing efficiency iscalculated as ratio of total volume of the primary packages within thesecondary package to the volume of corresponding secondary package.Furthermore, the method comprises packing each of the plurality ofsecondary packages within one or more tertiary packages based on MixedInteger Linear Programming (MILP) optimization model comprising anobjective function which maximizes space utilization within the one ormore tertiary packages, based on a plurality of heuristics, subject to aplurality of constraints including geometric constraints, orientationconstraints, stability constraints and tight packing constraints. Themethod further comprises calculating tertiary packing efficiency foreach of the one or more tertiary packages, wherein the tertiary packingefficiency is calculated as ratio of total volume of secondary packageswithin the tertiary package to volume of corresponding tertiary package.The method further comprises multiplying average of the secondarypacking efficiency of each of the subset of primary packages and averageof the tertiary packing efficiency of each of the one or more tertiarypackages to get a product of packing efficiencies; and selectingstandard secondary packages and corresponding clusters whose product ofpacking efficiencies is maximum, wherein the selected standard secondarypackages are utilized for packing newly obtained primary packages toachieve increased efficiency across packaging levels.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this disclosure, illustrate exemplary embodiments and, togetherwith the description, serve to explain the disclosed principles:

FIG. 1 illustrates an exemplary system for packing products withincreased efficiency across packaging levels according to someembodiments of the present disclosure.

FIG. 2 illustrates a functional flow of the system of FIG. 1 for packingof products with increased efficiency across packaging levels, accordingto some embodiments of the present disclosure.

FIGS. 3A, 3B and 3C, collectively referred as FIG. 3 depict an exemplaryflowchart illustrating method of packing of products with increasedefficiency across packaging levels, using the system of FIG. 1 ,according to some embodiments of the present disclosure.

FIG. 4 is an exemplary flowchart illustrating process of identifyingsecondary dimensions for a plurality of standard secondary packages,according to some embodiments of the present disclosure.

FIG. 5 illustrates mean tertiary packing efficiencies for experimentsconducted on a first dataset of secondary packages, according to someembodiments of present disclosure.

FIG. 6 illustrates mean tertiary packing efficiencies for experimentsconducted on a second dataset of secondary packages, according to someembodiments of present disclosure.

DETAILED DESCRIPTION

Exemplary embodiments are described with reference to the accompanyingdrawings. In the figures, the left-most digit(s) of a reference numberidentifies the figure in which the reference number first appears.Wherever convenient, the same reference numbers are used throughout thedrawings to refer to the same or like parts. While examples and featuresof disclosed principles are described herein, modifications,adaptations, and other implementations are possible without departingfrom the scope of the disclosed embodiments.

Referring now to the drawings, and more particularly to FIG. 1 through 6, where similar reference characters denote corresponding featuresconsistently throughout the figures, there are shown preferredembodiments and these embodiments are described in the context of thefollowing exemplary system and/or method.

FIG. 1 illustrates an exemplary system for packing products withincreased efficiency across packaging levels according to someembodiments of the present disclosure. In an embodiment, the system 100includes one or more processors 104, communication interface device(s)or Input/Output (I/O) interface(s) 106, and one or more data storagedevices or memory 102 operatively coupled to the one or more processors104. The memory 102 comprises a database 108. The one or more processors104 that are hardware processors can be implemented as one or moremicroprocessors, microcomputers, microcontrollers, digital signalprocessors, central processing units, state machines, logic circuitries,and/or any devices that manipulate signals based on operationalinstructions. Among other capabilities, the processor(s) is configuredto fetch and execute computer-readable instructions stored in thememory. In an embodiment, the system 100 can be implemented in a varietyof computing systems, such as laptop computers, notebooks, hand helddevices, workstations, mainframe computers, servers, a network cloud,and the like.

The I/O interface device(s) 106 can include a variety of software andhardware interfaces, for example, a web interface, a graphical userinterface, and the like and can facilitate multiple communicationswithin a wide variety of networks N/W and protocol types, includingwired networks, for example, LAN, cable, etc., and wireless networks,such as WLAN, cellular, or satellite. In an embodiment, the I/Ointerface device(s) can include one or more ports for connecting anumber of devices to one another or to another server.

The memory 102 may include any computer-readable medium known in the artincluding, for example, volatile memory, such as static random accessmemory (SRAM) and dynamic random access memory (DRAM), and/ornon-volatile memory, such as read only memory (ROM), erasableprogrammable ROM, flash memories, hard disks, optical disks, andmagnetic tapes. Further, the memory may include functional modules ofthe system as shown in FIG. 2 .

The database 108 may store information but not limited to, informationassociated with at least one of: (i) primary dimensions of a pluralityof primary packages and (ii) secondary dimensions of standard secondarypackages. Further, the database 108 stores information pertaining toinputs fed to the system 100 and/or outputs generated by the system(e.g., at each stage), specific to the methodology described herein.More specifically, the database 108 stores information of primarypackages and standardized secondary packages. Functions of thecomponents of system 100 are explained in conjunction with diagramsdepicted in FIGS. 2 through 5 for packing of products with increasedefficiency across packaging levels.

In an embodiment, the system 100 comprises one or more data storagedevices or the memory 102 operatively coupled to the processor(s) 104and is configured to store instructions for execution of steps of themethod depicted in FIG. 3 and process of the method depicted in FIG. 4by the processor(s) or one or more hardware processors 104. The steps ofthe method of the present disclosure will now be explained withreference to the components or blocks of the system 100 as depicted inFIG. 1 , functional flow diagram of the system 100 as depicted in FIG. 2and the steps of flow diagram as depicted in FIGS. 3 and 4 . Althoughprocess steps, method steps, techniques or the like may be described ina sequential order, such processes, methods and techniques may beconfigured to work in alternate orders. In other words, any sequence ororder of steps that may be described does not necessarily indicate arequirement that the steps to be performed in that order. The steps ofprocesses described herein may be performed in any order practical.Further, some steps may be performed simultaneously.

FIG. 2 illustrates a functional flow of the system of FIG. 1 for packingof products with increased efficiency across packaging levels, accordingto some embodiments of the present disclosure. The memory 102 of thesystem 100 comprises a crafter 202, a secondary packaging unit 206 and atertiary packaging unit 208. The database 108 includes a datasetcomprising primary dimensions of a plurality of primary packages. Thecrafter 202 periodically determines secondary dimensions of one or morestandard secondary packages for packing the plurality of primarypackages using a process 400 illustrated in FIG. 4 . During working ofthe system 100, one or more primary packages are transferred to thesecondary packaging unit 204 in an online fashion. Further, thesecondary packaging unit 204 packs each of the one or more primarypackages into suitable secondary packages having secondary dimensionsequal to one of the standard secondary packages. Further, the secondarypackaging unit 204 calculates secondary packing efficiency as ratio oftotal volume of the primary package within the secondary package to thevolume of corresponding secondary package. Further, the secondarypackages are transferred to the tertiary packaging unit 206 wherein thesecondary packages are packed into tertiary packages based on a MixedInteger Linear Programming (MILP) optimization model disclosed herein.Further, the tertiary packaging unit 206 calculates tertiary packingefficiency as ratio of total volume of the secondary packages within thetertiary package to the volume of corresponding tertiary package.Further, the secondary packing efficiency and tertiary packingefficiency are reported to the crafter 202 which periodically updatessecondary dimensions of standard secondary packages based on thesecondary and tertiary packing efficiencies.

FIGS. 3A, 3B and 3C, collectively referred as FIG. 3 depict an exemplaryflowchart illustrating a method 300 of packing of products withincreased efficiency across packaging levels, using the system of FIG. 1, according to some embodiments of the present disclosure. At step 302of the method 300, the one or more hardware processors 104 areconfigured to obtain, from the database 108, a dataset comprisingprimary dimensions of a plurality of primary packages, wherein theprimary dimensions include length, breadth, and height of each of theplurality of primary packages.

Further at step 304 of the method 300, the one or more hardwareprocessors 104 are configured to apply a clustering technique on theprimary dimensions of the plurality of primary packages to create aplurality of clusters of the plurality of primary packages. Each of theplurality of clusters has a subset of packages from the plurality ofprimary packages. In an embodiment, K-means clustering technique isapplied on the primary dimensions of the plurality of primary packageswherein value of K which denotes number of clusters to be created isequal to number of standard secondary packages required and can beconfigured by an operator of the system 100. While in state of the artK-Means clustering technique, each cluster is represented by thecentroid, the present disclosure represents each cluster by maximum ofeach primary dimension of the primary packages. This is done so that thesubset of primary packages within each cluster can fit within theprimary package representing the cluster. Due to this change in clusterrepresentation, objective function of the K-means clustering techniquealso changes. While in state of the art K-Means clustering technique theobjective function minimizes distance between the points within acluster and the centroid, the objective function of K-Means technique ofpresent disclosure minimizes sum ratio of volume of each of the subsetof primary packages within a cluster to the primary package representingthe cluster to achieve a high fill-rate (packing efficiency). Thesechanges in K-means clustering technique ensures a fill-rate of 70-77%for various datasets of primary dimensions of plurality of primarypackages with a median packing efficiency of around 72%.

Further at step 306 of the method 300, the one or more hardwareprocessors 104 are configured to identify secondary dimensions for aplurality of standard secondary packages, wherein each of the pluralityof standard secondary packages is associated with a correspondingcluster among the plurality of clusters and has the secondary dimensionsequal to maximum of each of the primary dimensions of the subset ofpackages within the corresponding cluster. Each of the subset of primarypackages within each of the plurality of clusters is packed, by thesecondary packaging unit 204, inside a secondary package havingsecondary dimensions equal to the standard secondary package ofcorresponding cluster. Thus, at the end of execution of step 306, thereare a plurality of secondary packages, each having a primary packagepacked within it.

The step 306 is further explained using the process 400 illustrated inFIG. 4 , according to some embodiments of the present disclosure. Atstep 402 of the process 400, a primary package with maximum primarydimensions from each of the plurality of clusters is selected. Theselected primary package is identified as initial standard secondarypackage for the corresponding cluster, and initial standard secondarypackages identified for each of the plurality of clusters together forma set of standard secondary packages. Further at step 404 of the process400, ratios of volume of each of the plurality of primary packages tovolume of each standard secondary package from the set of standardsecondary packages are calculated. Further, at step 406 of the process400, one or more standard secondary packages are identified from the setof standard secondary packages for each of the plurality of primarypackages based on conditions comprising—(i) calculated ratios of volumeis less than 1 and (ii) dimensions of the primary package is less thanthe dimensions of the secondary package. Further, at step 408 of theprocess 400, a final standard secondary package is selected, for each ofthe plurality of primary packages, among the one or more standardsecondary packages identified for each of the plurality of primarypackages. The selected final standard secondary package has least volumeamong the one or more standard secondary packages identified for each ofthe plurality of primary packages. Further, at step 410 of the process400, each of the plurality of primary packages are reassigned to thecluster corresponding to the selected final standard secondary package.

Thus, once the plurality of primary packages are reassigned to thecluster corresponding to the selected final standard secondary package,then referring back to steps of the method 300, at step 308 of themethod 300, the one or more hardware processors 104 are configured tocalculate secondary packing efficiency for each of the plurality ofsecondary packages. The secondary packing efficiency is calculated asratio of total volume of the primary package within the secondarypackage to the volume of corresponding secondary package.

Further at step 310 of the method 300, the one or more hardwareprocessors 104 are configured to pack the secondary packages within oneor more tertiary packages, via the tertiary packaging unit 206, based onMixed Integer Linear Programming (MILP) optimization model,alternatively referred as MILP model, comprising an objective functionwhich maximizes space utilization within the one or more tertiarypackages, based on a plurality of heuristics, subject to a plurality ofpacking constraints including geometric constraints, vertical stabilityconstraints, and efficient packing constraints. In an embodiment, theobjective function of the MILP optimization model is given by equation1.min{Σ_(iεP) _(L) (w ₁(x _(i) +y _(i))+w ₂· z _(l) +w ₃Σ_(j=1) ^(N) ^(B)p(i,j)·j)}   (1)

As understood by a person skilled in the domain, back left-bottom cornerof the tertiary package is treated as the origin. For each secondarypackage i placed inside a tertiary package, the coordinates (x_(i),y_(i), z_(i)) and (x_(l) , y_(l) , z_(l) ) denote the front-left-bottomand the back-right-top corners, respectively. As understood by a personskilled in the domain the points (x_(i), y_(i), z_(i)) and (x_(l) ,y_(l) , z_(l) ) uniquely determine the position of a secondary packageinside a tertiary package. In equation 1, P_(L) denotes set of secondarypackages to be packed within one or more tertiary packages;

${p\left( {i,j} \right)} = \left\{ {\begin{matrix}{1,{{if}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{placed}\mspace{14mu}{within}\mspace{14mu}{tertiary}\mspace{14mu}{package}\mspace{14mu} j}} \\{0,{otherwise}}\end{matrix};} \right.$and N_(B) denotes total number of currently open tertiary packages. Eachopen tertiary package is assigned an index j∈{1, 2, . . . J} where j<kwith j, k∈{1, 2, . . . N_(B)} implies that tertiary package j was openedbefore tertiary package k.

The objective function of equation 1 minimizes a sum of threecomponents—(i) w₁(x_(i)+y_(i)), (ii) w₂·z_(l) and (iii) w₃Σ_(j=1) ^(N)^(B) p(i,j). j representing floor building, column building andfirst-fit heuristic respectively. The first component follows floorbuilding heuristic by minimizing sum of x_(i) and y_(i) for a givensecondary package i thereby minimizing the spread of the secondarypackages on the floor. The second component follows column buildingheuristic by minimizing z_(l) thereby placing the secondary package i insuch a way that the overall height of packing arrangement afterconsidering all permissible orientations of the secondary package isminimized. The third component follows first-fit heuristic whereintertiary packages opened earlier are preferred over the tertiarypackages opened at a later point in time. The non-negative quantitiesw₁, w₂ and w₃ denote weight of the first, second and third componentrespectively. The first and second components act as countermeasures toeach other. The weights w₁ and w₂ denote which component is given moreimportance and these depend on the ratio of the height of the tertiarypackage to its base area. For instance, if the available tertiarypackages are roller-cages which have a larger height compared to theirbase area, then the weight w₁ is chosen higher than w₂. On the otherhand, if the tertiary package is a large flat long distance containerwith a larger base area and smaller height, then w₂ is chosen greaterthan w₁. Typically, value of w₃ is chosen very high (between 10 and 100)since the usual values of x_(i), y_(i) and z₁ in centimeters are 2orders of magnitude higher than p(i,j).

The MILP optimization model disclosed herein packs the secondarypackages by solving online bin packing problem, which is well known inthe art, as a series of offline bin packing problems. Suppose at time t∈

₀ there are

secondary packages (alternately referred as boxes in online bin packingproblem) in the look-ahead, N_(B) tertiary packages (alternatelyreferred as bins in online bin packing problem) are currently open, andN secondary packages are already placed in open tertiary packages. Theoffline bin packing problem is formulated as minimizing the objectivefunction described in equation 1 subject to a plurality of packingconstraints for the N+

secondary packages to be placed in N_(B) tertiary packages. However,since positions of secondary packages already placed within tertiarypackages cannot be changed, the parameters corresponding to thesecondary packages already placed within tertiary packages are updated.For example, suppose at time t=0, the MILP optimization model has toplace first

secondary packages into N_(B) open tertiary packages. Upon solving theMILP optimization model, a secondary package from P_(L) is placed intoone of the open tertiary package. Further, one more secondary package isadded to P_(L) so that

is constant. At t=1, the MILP optimization model consists of

(look-ahead)+1 (already in tertiary package) secondary packages withN_(B) open tertiary packages and the parameters corresponding to thesecondary package within the tertiary package are fixed to the valueobtained at t=0. This procedure is repeated iteratively. Though thenumber of secondary packages may increase, the number of open tertiarypackages is always ≤N_(B), and hence the MILP optimization model alwayssolves a finite optimization problem.

As understood by a person skilled in the domain, P_(B)={1, 2, . . . , N}denotes set of secondary packages already placed within one or moretertiary packages; P_(L)={1, 2, . . . ,

} denotes set of secondary packages in the look-ahead; and the set {1,2, . . . , N_(B)} denotes the set of tertiary packages open at aparticular instance of time. Every time a new tertiary package isopened, a tertiary package opened previously is closed and the indicesof the tertiary packages in the set of tertiary packages are reset. Asunderstood by a person skilled in the domain, following binary variablesare defined for all i, kϵP_(B)∪P_(L) (indices of secondary packages);j∈{1, 2, . . . , N_(B)} (indices of tertiary packages that are open);and s∈{x, y, z} (coordinates of secondary package within a tertiarypackage).

$\begin{matrix}{p_{i,j} = \left\{ \begin{matrix}{1,{{if}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{placed}\mspace{14mu}{within}\mspace{14mu}{tertiary}\mspace{14mu}{package}\mspace{14mu} j}} \\{0,{otherwise}}\end{matrix} \right.} & (2) \\{u_{j} = \left\{ \begin{matrix}{1,{{if}\mspace{14mu}{tertiary}\mspace{14mu}{package}\mspace{14mu} j\mspace{14mu}{was}\mspace{14mu}{used}}} \\{0,{otherwise}}\end{matrix} \right.} & (3) \\{s_{ik}^{p} = \left\{ \begin{matrix}{1,{{if}\mspace{14mu}{tertiary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{placed}\mspace{14mu}{at}\mspace{14mu}{right}\mspace{14mu}{of}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} k\mspace{14mu}\left( {{\overset{\_}{s}}_{k} \leq s_{i}} \right)}} \\{0,{{otherwise}\mspace{14mu}\left( {s_{i} < {\overset{\_}{s}}_{k}} \right)}}\end{matrix} \right.} & (4)\end{matrix}$

The variable s^(p) _(ik) as defined by equation 4 indicate relativeposition of secondary package i with respect to secondary package kalong the x, y and z axes, and ensures that the secondary packages i andk do not overlap each other inside a tertiary package. As understood bya person skilled in the domain, following binary variable is requiredfor specifying rotations allowed for placement of the secondarypackages.

$\begin{matrix}{r_{iab} = \left\{ \begin{matrix}{1,{{{if}\mspace{14mu} a\mspace{14mu}{side}\mspace{14mu} b\mspace{14mu}{of}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{along}\mspace{14mu} a} - {{axis}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{tertiary}\mspace{14mu}{package}}}} \\{0,{otherwise}}\end{matrix} \right.} & (5)\end{matrix}$

The variable r_(iab) is defined by equation 5 for every iϵP_(B)∪P_(L)and for each a, b∈{1, 2, 3}, and checks the degree of freedom of arobotic arm which is used to place a secondary package within a tertiarypackage. For example, if the length of the secondary package is placedalong the length of the tertiary package, then r_(i11)=1.

The plurality of packing constraints of the MILP optimization modelinclude geometric constraints, vertical stability constraints, andefficient packing constraints. The geometric constraints ensure thatplacement of secondary package inside tertiary package is geometricallyfeasible. The geometric constraints are defined by equations 6-13 forall iϵP_(B)∪P_(L), j∈{1, 2, . . . , N_(B)}, s∈{x, y, z} and a, b∈{1, 2,3}. The geometric constraints ensure that a tertiary package is usedonly if a secondary package is placed within the tertiary package, asecondary package is always placed within a tertiary package, andfeasible orientations of the secondary package are respected.Σ_(iϵP) _(B) _(∪P) _(L) p _(ij) ≤u _(j)  (6)Σ_(j=1) ^(B) p _(ij)=1  (7)ś _(l)≤Σ_(j=1) ^(B) L _(j) P _(ij)  (8)x _(l) −x _(i) =r _(i11) l _(i) +r _(i12) b _(i) +r _(i13) h _(i)  (9)y _(l) −y _(i) =r _(i21) l _(i) +r _(i22) b _(i) +r _(i23) h _(i)  (10)z _(l) −z _(i) =r _(i31) l _(i) +r _(i32) b _(i) +r _(i33) h _(i)  (11)Σ_(b) r _(iab)=1  (12)Σ_(a) r _(iab)=1  (13)Σ_(s∈{x,y,z})(s _(ik) ^(p) +s _(ki) ^(p))≥(p _(ij) +p _(kj))−1  (14)s _(k) ≤s _(i)+(1−s _(ik) ^(p))D  (15)s _(i)+1≤ s _(k) +s _(ik) ^(p) D  (16)

Equations 9-11 describe degrees of freedom the robotic arm has whileplacing a secondary package. The constraints defined by equations 14-16ensure that secondary packages do not overlap each other within atertiary package. The equations 14-16 are defined for all i,k∈P_(B)∪P_(L), j∈{1, 2, . . . , N_(B)}, s∈{x, y, z}, D=L, D=B and D=Hcorresponding to s=x, s=y and s=z respectively.

The vertical stability constraints of the MILP optimization model ensurethat there is a stable packing arrangement and the secondary packagebeing placed gets adequate support at the bottom and does not float inthe air. This is ensured by placing a secondary package either on thefloor of the tertiary package or in a location where at least 3 verticesof the base of the secondary package are supported by underlyingsecondary packages. As understood by a person skilled in the domain, avertex of secondary package i is said to be supported by anothersecondary package k, if its height is same as the base of the secondarypackage i and there is overlap between the two secondary packages in theX-Y plane. This is mathematically represented by variables g_(i) andβ_(ik) ^(l) which are declared according to equations 17 and 18 forevery i∈P_(L), k∈P_(B)∪P_(L), and l∈{1, 2, 3, 4} wherein l denotes basevertices of the secondary package i.

$\begin{matrix}{g_{i} = \left\{ \begin{matrix}{1,{{if}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{on}\mspace{14mu}{ground}\mspace{14mu}\left( {z_{i} = 0} \right)}} \\{0,{otherwise}}\end{matrix} \right.} & (17) \\{\beta_{ik}^{l} = \left\{ \begin{matrix}{1,{{if}\mspace{14mu}{vertex}\mspace{14mu} l\mspace{14mu}{of}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{supported}\mspace{14mu}{by}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} k}} \\{0,{otherwise}}\end{matrix} \right.} & (18)\end{matrix}$

The vertical stability constraints of the MILP optimization model areformulated according to equation 19 which ensures that sum of thevertices supported is either ≥0, when the secondary package is placed onthe floor of the container or ≥3, otherwise.Σ_(l=1) ⁴Σ_(k∈P) _(B) _(∪P) _(L) ,β_(ik) ^(l)≥3(1−g _(i)),∀∈P _(L)  (19)

The efficient packing constraints of the MILP optimization model ensurethat there are no gaps (or “holes”) in the packing arrangement toincrease fill-rate. This is achieved by ensuring that every feasiblelocation for a new secondary package at least two of the surfaces of thenew secondary package should either be touching the secondary packages(along the X-Y plane) already placed or the walls of the tertiarypackage. This is mathematically represented by variables d_(ikc) andd_(ijw) ^(w) which are declared according to equations 19 and 20 for alli∈P_(L), k∈P_(B)∪P_(L), j∈{1, 2, . . . , N_(B)}, c∈{x, y} and w∈{1, 2,3, 4} wherein l denotes base vertices of the secondary package i.

$\begin{matrix}{d_{ikc} = \left\{ \begin{matrix}{1,{{{if}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{in}\mspace{14mu}{contact}\mspace{14mu}{with}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} k\mspace{14mu}{along}\mspace{14mu} c} - {axis}}} \\{0,{otherwise}}\end{matrix} \right.} & (20) \\{d_{ijw}^{w} = \left\{ \begin{matrix}{1,{{if}\mspace{14mu}{secondary}\mspace{14mu}{package}\mspace{14mu} i\mspace{14mu}{is}\mspace{14mu}{in}\mspace{14mu}{contact}\mspace{14mu}{with}\mspace{14mu}{wall}\mspace{14mu} e\mspace{14mu}{of}\mspace{14mu}{tertiary}\mspace{14mu}{package}\mspace{14mu} j}} \\{0,{othewise}}\end{matrix} \right.} & (21)\end{matrix}$

The efficient packing constraints of the MILP optimization model areformulated according to equations 22-28 for every i∈P_(L),k∈P_(B)∪P_(L), j∈{1, 2, . . . , N_(B)}, c∈{x, y}. D=L, m=j, p=1, q=3 forc=x and D=B, m=1, p=3, q=4 for c=y.c _(i) ≤c _(k)+(1−d _(ikc))D  (22)c _(i) ≤c _(k)+(d _(ikc)−1)D  (23)c _(i)≤(m−1)D+(1−d _(ijp) ^(w))D  (24)c _(i)≤(m−1)D+(d _(ijp) ^(w)−1)D  (25)c _(i) ≤mD+(1−d _(ijq) ^(w))D  (26)c _(i) ≤mD+(d _(ijq) ^(w)−1)D  (27)Σ_(i∈P) _(L) Σ_(j=1) ^(N) ^(B) (d _(ij1) ^(w) +d _(ij3) ^(w))+Σ_(i∈P)_(L) Σ_(k∈P) _(B) _(∪P) _(L) d _(ikx)≤1  (28)Σ_(i∈P) _(L) Σ_(j=1) ^(N) ^(B) (d _(ij2) ^(w) +d _(ij4) ^(w))+Σ_(i∈P)_(L) Σ_(k∈P) _(B) _(∪P) _(L) d _(iky)≤1  (29)Σ_(i∈P) _(L) Σ_(j=1) ^(N) ^(B) Σ_(e=1) ⁴ d _(ije) ^(w)+Σ_(i∈P) _(L)Σ_(k∈P) _(B) _(∪P) _(L) Σ_(c∈{x,y}) d _(ikc)≥2  (30)

When a secondary package is being placed, the search for feasiblelocations has to guarantee the fact that at least two of its fourvertical surfaces will touch those of the secondary packages alreadyplaced inside the tertiary package and/or the walls of the tertiarypackage. However, there is also a need to remove redundancy within theformulation which may arise from counting the same surface twice if ittouches two or more secondary packages. These are guaranteed byconstraints in equations 28-30 which are defined by constraints inequations 22-27.

Thus, the MILP optimization model, as described above, enables packingof secondary packages inside one or more tertiary packages byiteratively identifying feasible locations for each secondary package inthe look-ahead and packing them within suitable tertiary package. If atany point in time, no feasible location for any of the secondary packageis identified, a tertiary package with maximum tertiary packingefficiency is closed and a new tertiary package is opened for packingthe remaining secondary packages.

Once process of tertiary packing is completed as in step 310, further atstep 312 of the method 300, the one or more hardware processors 104 areconfigured to calculate tertiary packing efficiency for each of the oneor more tertiary packages. The tertiary packing efficiency is calculatedas ratio of total volume of secondary packages within the tertiarypackage to volume of corresponding tertiary package.

Further at step 314 of the method 300, the one or more hardwareprocessors 104 are configured to multiply average of the secondarypacking efficiency of each of the subset of primary packages and averageof the tertiary packing efficiency of each of the one or more tertiarypackages to get a product of packing efficiencies.

Further at step 316 of the method 300, the one or more hardwareprocessors 104 are configured to select standard secondary packages, andcorresponding clusters whose product of packing efficiencies is maximum,wherein the selected standard secondary packages are utilized forpacking newly obtained primary packages to achieve increased efficiencyacross packaging levels.

Experimental Results

Fill-rates obtained by tertiary packaging based on Mixed Integer LinearProgramming (MILP) optimization model is compared with those offirst-fit heuristic, best-fit heuristic, Jampacker (M. Agarwal, S.Biswas, C. Sarkar, S. Paul and H. S. Paul, “Jampacker: An Efficient andReliable Robotic Bin Packing System for Cuboid Objects,” in IEEERobotics and Automation Letters, vol. 6, no. 2, pp. 319-326, April 2021,doi: 10.1109/LRA.2020.3043168) and MILP-Lite which is a variant of theMILP optimization model disclosed herein. The value of weights w₁, w₂and w₃ in the MILP optimization model are considered to be 1, 1, and 100respectively. The secondary packages are packed in online fashion usinga circular conveyor with a fixed

and a fixed N_(B)=3. The experiments have been performed on hardwarecomprising a laptop with a 4-core, i5-6200U processor with a speed of2.3 GHz and a memory of 4 GB.

Dataset Description

The experiments were performed on two datasets. The first datasetconsidered for the experiment consists of nearly a million secondarypackages which were packed in a sorting center over a period of oneyear. Initially, a smaller dataset was created by randomly sampling10,000 secondary packages from the dataset. Further, the secondarypackages are classified as small (65-80 secondary packages per tertiarypackage), medium (50-65 secondary packages per tertiary package), andlarge (35-50 secondary packages per tertiary package) depending on howmany secondary packages were required to optimally fill up a tertiarypackage. The size of tertiary package used was 120 cm×80 cm×80 cm.Twenty-five collections of secondary packages (with small, medium, andlarge packages mixed) were created by random sampling such thatsecondary packages from each collection would optimally fill 4 tertiarypackages. A crucial feature of this data-set is important: thedimensions of the secondary packages in most cases are not integers andhence, a ceiling function is used while placing the secondary packages.However, the results are reported on actual dimensions of the secondarypackages. The second dataset considered for the experiment issynthetically generated by identifying secondary dimensions of aplurality of secondary packages by dividing the 3-dimensional space of atertiary package (of size 80 cm×45 cm×45 cm) in such a way that whenpacked optimally the identified secondary packages would perfectly fitwithin the tertiary package. Care is taken so that the plurality ofsecondary packages are all cuboids; i.e., they are constructed bycutting planes that are orthogonal to each other. In addition to thesize of tertiary package considered (80 cm×45 cm×45 cm), experimentswith several others (mimicking industrial tertiary packages (bins) suchas roller-cages, pallets etc.) have been performed and the resultsobtained are consistent across all these tertiary packages.

Results and Analysis

FIG. 5 illustrates mean tertiary packing efficiencies for experimentsconducted on the first dataset of secondary packages, according to someembodiments of present disclosure. Table 1 represents the mean tertiarypacking efficiencies (across all 25 collections of secondary packages)for the first-fit heuristic, best-fit heuristic Jampacker, MILPoptimization model, and MILP-Lite. The first column of table 1 lists thetertiary packing method used and subsequent columns provide meantertiary packing efficiencies obtained for each tertiary packing methodwith look-ahead (

) of 1, 2, 3, 4, 5, and 6.

TABLE 1 Tertiary packing method

 = 1

 = 2

 = 3

 = 4

 = 5

 = 6 First-fit 64.91% 65.67% 67.42% 68.06% 69.18% 70.05% Best-fit 62.71%64.21% 64.71% 67.11% 66.67% 68.22% Jampacker 60.77% 62.11% 61.84% 61.57%61.38% 63.42% MILP 68.26% 69.99% 70.91% 71.29% 72.41% 72.89%optimization model MILP-Lite 68.01% 68.38% 69.06% 70.12% 70.2% 70.95%

The computation time for the first-fit, best-fit, and Jampack heuristicsis around (0.06-0.1 seconds per secondary package), but relatively morefor the MILP optimization model. Further, the computation time increaseswith the size of the MILP problem; i.e., with look-ahead (

). To alleviate this issue, alternate embodiments of present disclosureuse a “lite” version of MILP optimization model (referred as MILP-Lite)which decomposes a problem of

-look-ahead into

problems of 1-look-ahead. The computation time thus increases linearlywith look-ahead with marginal sacrifice of efficiency (as shown intables 1 and 2) whereas the computation time for the MILP optimizationmodel increases exponentially with increasing look-ahead. For instance,while the computation time jumps from 1.29 sec/secondary package to 3.22sec/secondary package to 10.71 sec/secondary package for

=2 to 4 for the MILP optimization model; for the MILP-lite, thecorresponding numbers are 1.3 sec/secondary package for

=2; 1.82 sec/secondary package for

=3; and 2.5 sec/secondary package for

=4. However, all of these computation times are well within the boundsof the robot decision-making operation (around 8-10 seconds persecondary package). From Table 1 and FIG. 5 , it can be inferred thatthe MILP optimization model (either original or lite version) achieves ahigher packing efficiency than other tertiary packing methods.

FIG. 6 illustrates mean tertiary packing efficiencies for experimentsconducted on the second dataset of secondary packages, according to someembodiments of present disclosure. Table 2 represents the mean tertiarypacking efficiencies for the first-fit heuristic, best-fit heuristicJampacker, MILP optimization model, and MILP-Lite. The first column oftable 1 lists the tertiary packing method used and subsequent columnsprovide mean tertiary packing efficiencies obtained for each tertiarypacking method with look-ahead (

) of 1, 2, 3, 4, 5, and 6.

TABLE 2 Tertiary packing method

 = 1

 = 2

 = 3

 = 4

 = 5

 = 6 First-fit  65.45% 66.49%  67.57% 68.485% 68.96% 69.555% Best-fit 68.71% 69.99% 70.435%  71.28% 71.74%  72.35% Jampacker  64.57% 65.22% 65.03%  64.77% 64.51%  65.43% MILP 73.925% 75.03% 75.945% 76.955%77.93%  78.32% optimization model MILP-Lite  73.11% 74.05%  74.83%  75.4% 75.99%  76.27%

From Table 2 and FIG. 6 it can be inferred that the MILP optimizationmodel and the MILP-Lite achieves a higher packing efficiency than othertertiary packing methods. Also, the packing efficiencies for the seconddataset is higher than those of the first dataset due to the nature ofdata in the dataset (dimensions are integers in the second datasetcompared to decimal dimensions and hence, the use of ceiling function inthe first dataset).

The written description describes the subject matter herein to enableany person skilled in the art to make and use the embodiments. The scopeof the subject matter embodiments is defined by the claims and mayinclude other modifications that occur to those skilled in the art. Suchother modifications are intended to be within the scope of the claims ifthey have similar elements that do not differ from the literal languageof the claims or if they include equivalent elements with insubstantialdifferences from the literal language of the claims.

The embodiments of present disclosure herein addresses unresolvedproblem of packing products with increased efficiency across packaginglevels. The embodiment thus provides a systematic and efficient methodof packing primary packages (or primary products) into secondary andtertiary packages. This is achieved by standardizing size of secondarypackages, packing the secondary packages within tertiary packages usingMILP optimization model based on packing heuristics, and providing afeedback between tertiary and secondary packaging levels to identifystandard secondary packages which can pack the primary packages withhigher packing efficiency. While the prior arts address improvingpacking efficiency in any one of the packaging levels, the presentdisclosure addresses all the levels of packaging and improves theoverall packing efficiency.

It is to be understood that the scope of the protection is extended tosuch a program and in addition to a computer-readable means having amessage therein; such computer-readable storage means containprogram-code means for implementation of one or more steps of themethod, when the program runs on a server or mobile device or anysuitable programmable device. The hardware device can be any kind ofdevice which can be programmed including e.g., any kind of computer likea server or a personal computer, or the like, or any combinationthereof. The device may also include means which could be e.g., hardwaremeans like e.g., an application-specific integrated circuit (ASIC), afield-programmable gate array (FPGA), or a combination of hardware andsoftware means, e.g., an ASIC and an FPGA, or at least onemicroprocessor and at least one memory with software processingcomponents located therein. Thus, the means can include both hardwaremeans and software means. The method embodiments described herein couldbe implemented in hardware and software. The device may also includesoftware means. Alternatively, the embodiments may be implemented ondifferent hardware devices, e.g., using a plurality of CPUs.

The embodiments herein can comprise hardware and software elements. Theembodiments that are implemented in software include but are not limitedto, firmware, resident software, microcode, etc. The functions performedby various components described herein may be implemented in othercomponents or combinations of other components. For the purposes of thisdescription, a computer-usable or computer readable medium can be anyapparatus that can comprise, store, communicate, propagate, or transportthe program for use by or in connection with the instruction executionsystem, apparatus, or device.

The illustrated steps are set out to explain the exemplary embodimentsshown, and it should be anticipated that ongoing technologicaldevelopment will change the manner in which particular functions areperformed. These examples are presented herein for purposes ofillustration, and not limitation. Further, the boundaries of thefunctional building blocks have been arbitrarily defined herein for theconvenience of the description. Alternative boundaries can be defined solong as the specified functions and relationships thereof areappropriately performed. Alternatives (including equivalents,extensions, variations, deviations, etc., of those described herein)will be apparent to persons skilled in the relevant art(s) based on theteachings contained herein. Such alternatives fall within the scope ofthe disclosed embodiments. Also, the words “comprising,” “having,”“containing,” and “including,” and other similar forms are intended tobe equivalent in meaning and be open ended in that an item or itemsfollowing any one of these words is not meant to be an exhaustivelisting of such item or items, or meant to be limited to only the listeditem or items. It must also be noted that as used herein and in theappended claims, the singular forms “a,” “an,” and “the” include pluralreferences unless the context clearly dictates otherwise.

Furthermore, one or more computer-readable storage media may be utilizedin implementing embodiments consistent with the present disclosure. Acomputer-readable storage medium refers to any type of physical memoryon which information or data readable by a processor may be stored.Thus, a computer-readable storage medium may store instructions forexecution by one or more processors, including instructions for causingthe processor(s) to perform steps or stages consistent with theembodiments described herein. The term “computer-readable medium” shouldbe understood to include tangible items and exclude carrier waves andtransient signals, i.e., be non-transitory. Examples include randomaccess memory (RAM), read-only memory (ROM), volatile memory,nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, andany other known physical storage media.

It is intended that the disclosure and examples be considered asexemplary only, with a true scope of disclosed embodiments beingindicated by the following claims.

What is claimed is:
 1. A process implemented method for packing productsby online bin packing with increased efficiency across packaging levels,the method comprising: obtaining, by one or more hardware processors, adataset comprising primary dimensions of a plurality of primarypackages, wherein the primary dimensions include length, breadth, andheight of each of the plurality of primary packages; applying, by theone or more hardware processors, a K-means clustering technique on theprimary dimensions of the plurality of primary packages to create aplurality of clusters of the plurality of primary packages, wherein eachof the plurality of clusters has a subset of packages from the pluralityof primary packages, wherein each of the plurality of clusters isrepresented by maximum of each of the primary dimensions of the subsetof packages within a corresponding cluster among the plurality ofclusters, wherein the K-means clustering technique comprises anobjective function to minimize sum ratio of volume of each of the subsetof primary packages within the corresponding cluster to a standardpackage representing the corresponding cluster having dimensions equalto maximum of each of the primary dimensions of the subset of packageswithin the corresponding cluster and achieves a high packing efficiency;identifying, by the one or more hardware processors, secondarydimensions for a plurality of standard secondary packages for theplurality of clusters, wherein each of the plurality of standardsecondary packages is associated with the corresponding cluster and hasthe secondary dimensions equal to maximum of each of the primarydimensions of the subset of packages within the corresponding cluster,and wherein each of the subset of primary packages within each of theplurality of clusters is packed inside a secondary package havingsecondary dimensions equal to the standard secondary package ofcorresponding cluster to generate a plurality of secondary packages, andwherein the secondary dimension of the plurality of secondary packagesare identified by dividing a 3-Dimensional space of a tertiary packagein such a way that when packed optimally the identified secondarypackages perfectly fits within the tertiary package, wherein thesecondary dimension of the plurality of secondary packages areidentified by: selecting a final standard secondary package, for each ofthe plurality of primary packages, among the one or more standardsecondary packages identified for each of the plurality of primarypackages, wherein the selected final standard secondary package hasleast volume among the one or more standard secondary packagesidentified for each of the plurality of primary packages; andreassigning each of the plurality of primary packages to the clustercorresponding to the selected final standard secondary package;calculating, by the one or more hardware processors, secondary packingefficiency for each of the plurality of secondary packages, wherein thesecondary packing efficiency is calculated as ratio of total volume ofthe primary package within the secondary package to the volume ofcorresponding secondary package; packing, by a robotic arm via the oneor more hardware processors, the plurality of secondary packages withinone or more tertiary packages using Mixed Integer Linear Programming(MILP) optimization model, wherein the robotic arm picks and places theplurality of secondary packages in the one or more tertiary packages,wherein the MILP comprises an objective function which maximizes spaceutilization within the one or more tertiary packages, based on aplurality of heuristics and checks a degree of freedom of the roboticarm that is used to place the secondary package within the tertiarypackage, subject to a plurality of packing constraints comprisinggeometric constraints, vertical stability constraints, and efficientpacking constraints, and wherein the MILP optimization model enablespacking by: iteratively identifying feasible locations for each of theplurality of secondary packages in look-ahead and packing the pluralityof secondary packages within suitable tertiary package, if at any pointin time, no feasible location for the secondary packages is identified,a tertiary package with maximum tertiary packing efficiency is closedand a new tertiary package is opened for packing remaining secondarypackages, wherein the MILP optimization model decomposes a problem of

-look-ahead into

problems of 1-look-ahead to reduce the computation time of the MILPoptimization model, and wherein the computation time of the MILPoptimization model is within a time bound of a robot decision-makingoperation for picking and placing the plurality of secondary packages inthe one or more tertiary packages; and providing a feedback between thetertiary package and the secondary packages to identify standardsecondary packages which can pack the primary packages with higherpacking efficiency; calculating, by the one or more hardware processors,tertiary packing efficiency for each of the one or more tertiarypackages, wherein the tertiary packing efficiency is calculated as ratioof total volume of secondary packages within the tertiary package tovolume of corresponding tertiary package; multiplying, by the one ormore hardware processors, an average of the secondary packing efficiencyof each of the plurality of secondary packages and an average of thetertiary packing efficiency of each of the one or more tertiary packagesto get a product of packing efficiencies; and selecting, by the one ormore hardware processors, the standard secondary packages, andcorresponding clusters whose product of packing efficiencies is maximum,wherein the selected standard secondary packages are utilized forpacking newly obtained primary packages to achieve increased efficiencyacross packaging levels.
 2. The method as claimed in claim 1, whereinidentifying the secondary dimensions for a plurality of standardsecondary packages is further performed by: selecting the primarypackage with maximum primary dimensions from each of the plurality ofclusters, wherein the selected primary package is identified as aninitial standard secondary package for the corresponding cluster, andwherein initial standard secondary packages identified for each of theplurality of clusters together form a set of standard secondarypackages; calculating ratios of volume of each of the plurality ofprimary packages to volume of each of the set of standard secondarypackages; and identifying one or more standard secondary packages fromthe set of standard secondary packages for each of the plurality ofprimary packages based on conditions comprising—(i) calculated ratios ofvolume is less than 1 and (ii) dimensions of the primary package is lessthan the dimensions of the secondary package.
 3. The method as claimedin claim 1, wherein the one or more heuristics include a floor buildingheuristic, a column building heuristic, and a first fit heuristic. 4.The method as claimed in claim 3, wherein the floor building heuristicaims to minimize overall height of the tertiary packing arrangement byplacing the one or more standard secondary packages on floor of thetertiary package in a tightly arranged layer-by-layer approach, whereinthe secondary packages are placed at the lowest possible heightrespecting the stability constraints, and wherein if no such location isidentified for all allowed orientations of the secondary package, a newtertiary package is opened and the secondary package is placed withinthe new tertiary package.
 5. The method as claimed in claim 3, whereinthe column building heuristic aims to maximize overall height of thetertiary packing arrangement by stacking secondary packages on top ofeach other, wherein, the secondary package is placed at maximum possibleheight identified for any allowed orientation respecting the stabilityconstraints and wherein if no such location is identified for allallowed orientations of the secondary package, a new tertiary package isopened and the secondary package is placed within the new tertiarypackage.
 6. The method as claimed in claim 3, wherein the first-fitheuristic places the secondary package into a tertiary package that isopened first, wherein for a given secondary package in a certainorientation, the first-fit heuristic identifies a feasible locationsatisfying the plurality of stability constraints by scanning row by rowfrom origin of the tertiary package and if such a location is notidentified, orientation of the standard secondary package is changed,and the scanning procedure is repeated, wherein if no feasible locationexists for all permissible orientations, the scanning procedure moves tothe tertiary package which is opened in succession, and wherein if noneof the opened tertiary packages have a feasible location, a new tertiarypackage is opened and the secondary package is placed within the newtertiary package.
 7. A system for packing products by online bin packingwith increased efficiency across packaging levels, comprising: a memorystoring instructions; one or more communication interfaces; and one ormore hardware processors coupled to the memory via the one or morecommunication interfaces, wherein the one or more hardware processorsare configured by the instructions to: obtain a dataset comprisingprimary dimensions of a plurality of primary packages, wherein theprimary dimensions include length, breadth, and height of each of theplurality of primary packages; apply a K-means clustering technique onthe primary dimensions of the plurality of primary packages to create aplurality of clusters of the plurality of primary packages, wherein eachof the plurality of clusters has a subset of packages from the pluralityof primary packages, wherein each of the plurality of clusters isrepresented by maximum of each of the primary dimensions of the subsetof packages within a corresponding cluster among the plurality ofclusters, wherein the K-means clustering technique comprises anobjective function to minimize sum ratio of volume of each of the subsetof primary packages within the corresponding cluster to a standardpackage representing the corresponding cluster having dimensions equalto maximum of each of the primary dimensions of the subset of packageswithin the corresponding cluster and achieves a high packing efficiency;identify secondary dimensions for a plurality of standard secondarypackages for the plurality of clusters, wherein each of the plurality ofstandard secondary packages is associated with the corresponding clusterand has the secondary dimensions equal to maximum of each of the primarydimensions of the subset of packages within the corresponding cluster,and wherein each of the subset of primary packages within each of theplurality of clusters is packed inside a secondary package havingsecondary dimensions equal to the standard secondary package ofcorresponding cluster to generate a plurality of secondary packages, andwherein the secondary dimension of the plurality of secondary packagesare identified by dividing a 3-Dimensional space of a tertiary packagein such a way that when packed optimally the identified secondarypackages perfectly fits within the tertiary package, wherein thesecondary dimension of the plurality of secondary packages areidentified by: selecting a final standard secondary package, for each ofthe plurality of primary packages, among the one or more standardsecondary packages identified for each of the plurality of primarypackages, wherein the selected final standard secondary package hasleast volume among the one or more standard secondary packagesidentified for each of the plurality of primary packages; andreassigning each of the plurality of primary packages to the clustercorresponding to the selected final standard secondary package;calculate secondary packing efficiency for each of the plurality ofsecondary packages, wherein the secondary packing efficiency iscalculated as ratio of total volume of the primary package within thesecondary package to the volume of corresponding secondary package;pack, by a robotic arm, the plurality of secondary packages within oneor more tertiary packages using Mixed Integer Linear Programming (MILP)optimization model, wherein the robotic arm picks and places theplurality of secondary packages in the one or more tertiary packages,wherein the MILP comprises an objective function which maximizes spaceutilization within the one or more tertiary packages, based on aplurality of heuristics and checks a degree of freedom of the roboticarm that is used to place the secondary package within the tertiarypackage, subject to a plurality of packing constraints comprisinggeometric constraints, vertical stability constraints, and efficientpacking constraints, and wherein the MILP optimization model enablespacking by: iteratively identifying feasible locations for each of theplurality of secondary packages in look-ahead and packing the pluralityof secondary packages within suitable tertiary package, if at any pointin time, no feasible location for the secondary packages is identified,a tertiary package with maximum tertiary packing efficiency is closedand a new tertiary package is opened for packing remaining secondarypackages, wherein the MILP optimization model decomposes a problem of

-look-ahead into

problems of 1-look-ahead to reduce the computation time of the MILPoptimization model, and wherein the computation time of the MILPoptimization model is within a time bound of a robot decision-makingoperation for picking and placing the plurality of secondary packages inthe one or more tertiary packages; and providing a feedback between thetertiary package and the secondary packages to identify standardsecondary packages which can pack the primary packages with higherpacking efficiency; calculate tertiary packing efficiency for each ofthe one or more tertiary packages, wherein the tertiary packingefficiency is calculated as ratio of total volume of secondary packageswithin the tertiary package to volume of corresponding tertiary package;multiply an average of the secondary packing efficiency of each of theplurality of secondary packages and an average of the tertiary packingefficiency of each of the one or more tertiary packages to get a productof packing efficiencies; and select standard secondary packages, andcorresponding clusters whose product of packing efficiencies is maximum,wherein the selected standard secondary packages are utilized forpacking newly obtained primary packages to achieve increased efficiencyacross packaging levels.
 8. The system as claimed in claim 7, whereinthe one or more hardware processors are further configured by theinstructions to identify the secondary dimensions for a plurality ofstandard secondary packages by: selecting the primary package withmaximum primary dimensions from each of the plurality of clusters,wherein the selected primary package is identified as an initialstandard secondary package for the corresponding cluster, and whereininitial standard secondary packages identified for each of the pluralityof clusters together form a set of standard secondary packages;calculating ratios of volume of each of the plurality of primarypackages to volume of each of the set of standard secondary packages;and identifying one or more standard secondary packages from the set ofstandard secondary packages for each of the plurality of primarypackages based on conditions comprising—(i) calculated ratios of volumeis less than 1 and (ii) dimensions of the primary package is less thanthe dimensions of the secondary package.
 9. The system as claimed inclaim 7, wherein the one or more heuristics include a floor buildingheuristic, a column building heuristic, and a first fit heuristic. 10.The system as claimed in claim 9, wherein the floor building heuristicaims to minimize overall height of the tertiary packing arrangement byplacing the one or more standard secondary packages on floor of thetertiary package in a tightly arranged layer-by-layer approach, whereinthe secondary packages are placed at the lowest possible heightrespecting the stability constraints, and wherein if no such location isidentified for all allowed orientations of the secondary package, a newtertiary package is opened and the secondary package is placed withinthe new tertiary package.
 11. The system as claimed in claim 9, whereinthe column building heuristic aims to maximize overall height of thetertiary packing arrangement by stacking secondary packages on top ofeach other, wherein, the secondary package is placed at maximum possibleheight identified for any allowed orientation respecting the stabilityconstraints and wherein if no such location is identified for allallowed orientations of the secondary package, a new tertiary package isopened and the secondary package is placed within the new tertiarypackage.
 12. The system as claimed in claim 9, wherein the first-fitheuristic places the secondary package into a tertiary package that isopened first, wherein for a given secondary package in a certainorientation, the first-fit heuristic identifies a feasible locationsatisfying the plurality of stability constraints by scanning row by rowfrom origin of the tertiary package and if such a location is notidentified, orientation of the standard secondary package is changed,and the scanning procedure is repeated, wherein if no feasible locationexists for all permissible orientations, the scanning procedure moves tothe tertiary package which is opened in succession, and wherein if noneof the opened tertiary packages have a feasible location, a new tertiarypackage is opened and the secondary package is placed within the newtertiary package.
 13. One or more non-transitory machine readableinformation storage mediums comprising one or more instructions whichwhen executed by one or more hardware processors cause: obtaining, byone or more hardware processors, a dataset comprising primary dimensionsof a plurality of primary packages, wherein the primary dimensionsinclude length, breadth, and height of each of the plurality of primarypackages; applying, by the one or more hardware processors, a clusteringtechnique on the primary dimensions of the plurality of primary packagesto create a plurality of clusters of the plurality of primary packages,wherein each of the plurality of clusters has a subset of packages fromthe plurality of primary packages, wherein each of the plurality ofclusters is represented by maximum of each of the primary dimensions ofthe subset of packages within a corresponding cluster among theplurality of clusters, wherein the K-means clustering techniquecomprises an objective function to minimize sum ratio of volume of eachof the subset of primary packages within the corresponding cluster to astandard package representing the corresponding cluster havingdimensions equal to maximum of each of the primary dimensions of thesubset of packages within the corresponding cluster and achieves a highpacking efficiency; identifying, by the one or more hardware processors,secondary dimensions for a plurality of standard secondary packages forthe plurality of clusters, wherein each of the plurality of standardsecondary packages is associated with the corresponding cluster and hasthe secondary dimensions equal to maximum of each of the primarydimensions of the subset of packages within the corresponding cluster,and wherein each of the subset of primary packages within each of theplurality of clusters is packed inside a secondary package havingsecondary dimensions equal to the standard secondary package ofcorresponding cluster to generate a plurality of secondary packages, andwherein the secondary dimension of the plurality of secondary packagesare identified by dividing a 3-Dimensional space of a tertiary packagein such a way that when packed optimally the identified secondarypackages perfectly fits within the tertiary package, wherein thesecondary dimension of the plurality of secondary packages areidentified by: selecting a final standard secondary package, for each ofthe plurality of primary packages, among the one or more standardsecondary packages identified for each of the plurality of primarypackages, wherein the selected final standard secondary package hasleast volume among the one or more standard secondary packagesidentified for each of the plurality of primary packages; andreassigning each of the plurality of primary packages to the clustercorresponding to the selected final standard secondary package;calculating, by the one or more hardware processors, secondary packingefficiency for each of the plurality of secondary packages, wherein thesecondary packing efficiency is calculated as ¬¬-ratio of total volumeof the primary package within the secondary package to the volume ofcorresponding secondary package; packing, by a robotic arm via the oneor more hardware processors, the plurality of secondary packages withinone or more tertiary packages using Mixed Integer Linear Programming(MILP) optimization model, wherein the robotic arm picks and places theplurality of secondary packages in the one or more tertiary packages,wherein the MILP comprises an objective function which maximizes spaceutilization within the one or more tertiary packages, based on aplurality of heuristics and checks a degree of freedom of the roboticarm that is used to place the secondary package within the tertiarypackage, subject to a plurality of packing constraints comprisinggeometric constraints, vertical stability constraints, and efficientpacking constraints, and wherein the MILP optimization model enablespacking by: iteratively identifying feasible locations for each of theplurality of secondary packages in look-ahead and packing the pluralityof secondary packages within suitable tertiary package, if at any pointin time, no feasible location for the secondary packages is identified,a tertiary package with maximum tertiary packing efficiency is closedand a new tertiary package is opened for packing remaining secondarypackages, wherein the MILP optimization model decomposes a problem of

-look-ahead into

problems of 1-look-ahead to reduce the computation time of the MILPoptimization model, and wherein the computation time of the MILPoptimization model is within a time bound of a robot decision-makingoperation for picking and placing the plurality of secondary packages inthe one or more tertiary packages; and providing a feedback between thetertiary package and the secondary packages to identify standardsecondary packages which can pack the primary packages with higherpacking efficiency; calculating, by the one or more hardware processors,tertiary packing efficiency for each of the one or more tertiarypackages, wherein the tertiary packing efficiency is calculated as ratioof total volume of secondary packages within the tertiary package tovolume of corresponding tertiary package; multiplying, by the one ormore hardware processors, an average of the secondary packing efficiencyof each of the plurality of secondary packages and an average of thetertiary packing efficiency of each of the one or more tertiary packagesto get a product of packing efficiencies; and selecting, by the one ormore hardware processors, standard secondary packages, and correspondingclusters whose product of packing efficiencies is maximum, wherein theselected standard secondary packages are utilized for packing newlyobtained primary packages to achieve increased efficiency acrosspackaging levels.